Correlation of Aggregate Form Properties with Fourier Frequencies

Abstract

Aggregate morphology consists of three independent components: form, angularity, and surface texture. As these three components act in different ways in affecting the performance of pavement layer, it is vital to characterize them objectively and accurately. In this study, the coordinates of boundary pixels of aggregate from 2-D images were treated as an equally spaced complex series. The description of the aggregate shape in the frequency domain was obtained by analyzing this complex series with the discrete Fourier transform (DFT). Based on this, the reconstruction of aggregate shape at different frequencies was performed, which validated that the three elements of aggregate shape correspond to different frequencies. In addition, by fitting the relationship between DFT coefficients and form parameters (elongation ratio, sphericity, mean radius, variance of radius), the frequencies contributing to the form properties of aggregate were identified. Moreover, prediction models for the elongation ratio, sphericity, mean, and variance of radius based on the DFT coefficients at the contributing frequencies were developed separately.

Characterization of Aggregate Angularity in the Frequency Domain

“…Specifically: form refers to the large variations of proportion; angularity captures the medium variations at corners that are superimposed on the form, surface texture describes the small surface irregularities that are too minor to affect the overall aggregate shape (1)(2)(3)(4). In addition to the differences in scale, these three elements also represent different frequencies, where the form corresponds to low frequency and high amplitude elements, angularity corresponds to medium frequency and amplitude elements, and the surface texture corresponds to high frequency and the lowest amplitude elements (5). Because the scale and frequency of each of these three elements act independently of the others, each of them can vary significantly without necessarily imposing influence on the others (6,7).…”

“…Aggregate characteristics are critically important for pavement performance. Within different pavement layers, the discretely distributed aggregates can form a skeleton network through stone-to-stone contact and interlock ( 5 ). This skeleton is essential for the pavement to support traffic loading.…”

“…Based on the Fourier analysis of the radius-angle description of the aggregate shape, Wettimuny et al ( 19 ) developed a procedure to quantitatively characterize the roundness and angularity of the aggregate shape. However, this method had limitations in relation to accounting for aggregate shapes with a single radial vector that might encounter two boundaries when radiating from the centroid ( 1, 5 ). Also based on the Fourier transform of the radius-angle description of aggregate shapes, Wang et al ( 8 ) proposed a unified method to characterize form, angularity, and surface texture by calculating the sum of the square of the Fourier coefficients within corresponding frequency ranges.…”

“…The method was proved to be reliable by comparing its results with those of other available systems. In another research study using regression analysis ( 5 ), the authors successfully identified the frequencies corresponding to aggregate forms and developed reliable models for different form parameters.…”